Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 7 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Belief Degrees | Belief degree, degree of belief: subjective assessment of the likelihood of an event. See also belief, probability, probability theory, Bayesianism, Principal Principle, subjective probability. |
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| Humean World | Lewis | V IX Humean supervenience/HS/Lewis: Thesis: everything in the world is a large mosaic of local facts - there is a geometry: a system of external relations of spatiotemporal distances between points - at the points we have local qualities, perfectly natural intrinsic properties - everything is an arrangement of qualities (AoQ). Everything supervenes on it. Important argument: there is no distinction without difference. - That does not mean that two possible worlds could not be different without having a difference in the AoQ. Cf. >Causality/Hume. Example 1) possible worlds with Humean supervenience, 2) possible worlds without! - ((s) i.e. Humean supervenience is contingent). Lewis: for our inner sphere of possibilities there is no such distinction. V VII Arrow of time: only in one direction - the Humean supervenience has to consider this asymmetry. - Humean supervenience/(s): does not mean here that causality is denied. --- V X Materialism/Humean supervenience/Lewis: materialism is a metaphysics that is to confirm the truth of known physics. Humean supervenience: it may be that the Humean supervenience is true and all our physics wrong. V 111 Humean supervenience/Coincidence/Lewis: If the Humean supervenience is wrong, there is a fatal counter e.g., which is made by coincidences - then coincidences and coincidence theories do not supervene on facts. Problem: a theory of coincidence is not something that itself may only have a certain chance - (which also says the Principal Principle PP) - an equally likely deviant pattern would lead to an entirely different coincidence theory. Right: chances are contingent because they depend on contingent facts, but not because they depended on a theory of coincidence - then the Humean supervenience is maintained. --- Schwarz I 112 Humean supervenience/Lewis/Schwarz: From description which property exists at point X and which at point y we learn which properties these are, thus in which the laws of nature apply. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Likelihood | Schurz | I 160 Likelihood/Likelihood Intuition/L Intuition/Schurz: according to this intuition, the inverse likelihood p(E : H) is the basic criterion for assessing the plausibility of a hypothesis H given outcome E. Terminology: sometimes this is called inverse likelihood: p(E : H). Likelihood Intuition/Schurz: is not to be confused with the likelihood method, but it is much more basic. Method of likelihood maximization: here it is assumed that the higher the likelihood of E given H, the greater the support of a hypothesis H by an evidence E. Likelihood expectation method: here it is assumed that the support of a hypothesis by an evidence E is greater, the closer E is to the expected value of E formed with the likelihoods of E given H. Point method/Interval method/Likelihood/Schurz: can be further distinguished. Statistics/Philosophy/Schurz: the philosophical problem is much deeper: one can consider statistical inference and testing methods as justified only if one considers the likelihood intuition as justified. >Review/Schurz. I 161 Why should inverse probability be considered as a measure of the plausibility of a hypothesis? There is no answer to this within statistical theory. Because plausibility is a subjective epistemic probability w(H I E) about which statistical theory makes no statements. Likelihood intuition/subjective probability/Schurz: within subjective probability theory, the likelihood intuition is explained by the Principal Principle (correspondence of subjective with objective probability, if the latter is known). >Principal Principle. >Bayes-theorem, >Probability, >Probability theory, >Propensity, >Subjective probability. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Probability | Lewis | V 83 Probability/subjectivism/subjective probability/Lewis: pro subjectivism: beliefs about probabality are relevant. - Only subjectivism can understand them. V 85 It is possible that we also believe from a coin which showed 85% head in the past that the chance next time is 50%. Resilience/Skyrms: Elasticity: uncertainty cannot be shaken by new information. - Beliefs about results and prospects may differ. V 89 Solution: The chance of t that A is true is a non-rigid designator. V 86 Believe/reasonable/probability/opportunities/Lewis: Degrees of believe about results that are based on certainty of chances are elastic (resilient, relatively immune to new information) if the new information is permissible (i.e. after the event). V 86 Principal Principle/main principle/probability/opportunity/Lewis: the Principal Principle is to be modeled according to our experience with direct conclusions. >Terminologie/Lewis. Exceptions: 1) it is about opportunity, not frequency. 2) Certainty of probabilities (opportunities) contributes to the resilience (resistance to new information). V 147 Probability/Lewis: is shifted. - Never created or destroyed. - So the sum is always 1. >Chance/Lewis, >Likelihood/Lewis. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| Probability Theory | Schurz | I 110 Probability theory/theorems/Schurz: a) unconditioned probability: (objective und subjective) (T1) p(~A) = 1 – p(A) (complementary probability) (T2) p(A) ≤ 1 (upper bound) (T3) p(A u ~A) = 0 (contradiction) (T4) p(A1 v A2) = p(A1) + p(A2) – p(A1 u A2) (general law of addition). b) conditioned probability (for formulas X in antecedens position) (PT1) If B > A is exhaustive, gilt p(A I B) = 1. The converse is not valid. (PT2) p(A u B) = p(A I B) mal p(B) (PT3) Für jede Partition B1,...Bn: p(A) = ∑ 1≤i≤n p(A I Bi) times p(Bi) (general law of multiplication) (PT4): Def Bayes-Theorem, 1st version: p(A I B) = p(B I A) times p(A)/p(B) (PT5) Def Bayes-Theorem, 2nd version: for each partition A1,...An: p(Ai I B) = p(B I Ai) times p (Ai) /∑ 1≤i≤n p(B I Ai) times p(Ai). (PT6) Symmetry of probabilistic dependence: p(A I B) > p(A) iff p(B I A) > p(B) iff p(B I A) > p(B I ~A) (analog for ≥). Def Partition/Schurz: exhaustive disjunction. I 110 Consequence relation/probability/consequence/probability theory/Schurz: the probability-theoretic inference relation can be characterized as follows: a probability statement A follows probabilistically from a set D of probability statements iff. A follows logically from D and the Kolmogorov axioms (plus mathematical definitions). >Probability. I 112 Probability theory/Schurz: still unsolved problems: (a) objective probability: definitional problems. Definition of statistical probability: problem: with one random experiment one can potentially produce infinitely many infinitely increasing sequences of results, Why should they all have the same frequency limit? Why should they have one at all? Problem: even worse: from a given sequence of results, one can always construct a sequence with an arbitrarily deviating frequency limit value by arbitrary rearrangement or place selection. I 113 Law of large numbers/Schurz: ("naive statistical theory"): is supposed to be a solution for this problem: the assertion "p(Fx) = r" does not say then that in all random sequences the frequency limit is r, but only that it is r with probability 1. StegmüllerVs/KutscheraVs: This is circular! In the definiens of the expression "the probability of Fx is r" the expression "with probability 1" occurs again. Thus the probability is not reduced to frequency limits, but again to probability. >Circularity. Rearrangement/(s): only a problem with infinite sets, not with finite ones. Mises/solution: "statistical collective". 1. every possible outcome E has a frequency threshold in g, identified with probability p(E), and 2. this is insensitive to job selection. From this follows the general product rule/statistic: the probability of a sum is equal to the product of the individual probabilities: p(Fx1 u Gx2) = p(Fx1) times p(Gx2). Probability /propensity//Mises: this result of Mises is empirical, not a priori! It is a substantive dispositional statement about the real nature of the random experiment (>Ontology/Statistics). The Mises probability is also called propensity. >Propensity. Singular Propensity/Single Case Probability/Single Probability/Popper: many Vs. Probability theory/Schurz: problem: what is the empirical content of a statistical hypothesis and how is it tested? There is no observational statement that logically follows from this hypothesis. >Verification. That a random sequence has a certain frequency limit r is compatible for any n, no matter how large, with any frequency value hn unequal to r reached up to that point. Bayes/Schurz: this is often raised as an objection by Bayesians, but it merely expresses the fact that no observational theorems follow from statistical hypotheses. I 115 Verification/Statistics/Schurz: Statistical hypotheses are not deductively testable, but they are probabilistically testable, by sampling. I 115 Principal Principle/PP/Statistics/Schurz: subjective probabilities, if objective probabilities are known, must be consistent with them. Lewis (1980): singular PP: subjectivist. Here "objective" singular propensities are simply postulated. >Propensities. SchurzVsPropensity/SchurzVsPopper: it remains unclear what property a singular propensity should correspond to in the first place. Solution/de Finetti: one can also accept the objective notion of probability at the same time. Conditionalization/Statistics/Schurz: on an arbitrary experience datum E(b1...bn) over other individuals b1,..bn is important to derive two further versions of PP: 1. PP for random samples, which is needed for the subjective justification of the statistical likelihood intuition. 2. the conditional PP, for the principle of the closest reference class and subject to the inductive statistical specialization inference. PP: w(Fa I p(Fx) = r u E(b1,...bn)) = r PP for random samples: w(hn(Fx) = k/n I p(Fx) = r) = (nk) rk times (1 r)n k. Conditional PP: w(Fa I Ga u p(Fx I Gx) = r u E(b1,...bn)) = r. Principal principle: is only meaningful for subjective a priori probability. I.e. degrees of belief of a subject who has not yet had any experience. Actual degree of belief: for him the principle does not apply in general: e.g. if the coin already shows heads, (=Fa) so the act. dgr. of belief of it is of course = 1, while one knows that p(Fx) = ½. a priori probability function: here all background knowledge W must be explicitly written into the antecedent of a conditional probability statement w( I W). Actual: = personalistic. Apriori probability: connection with actual probability: Strict conditionalization/Schurz: let w0 be the a priori probability or probability at t0 and let w1 be the actual probability I 116 Wt the knowledge acquired between t0 and t1. Then for any A holds: Wt(A) = w0(A I Wt). Closest reference class/principle/Schurz: can be justified in this way: For a given event Fa, individual a can belong to very many reference classes assigning very different probabilities to Fx. Then we would get contradictory predictions. Question: But why should the appropriate reference class be the closest one? Because we can prove that it maximizes the frequency threshold of accurate predictions. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Subjective Probability | Schurz | I 99 Def Objective probability/Schurz: the probability of an event type (e.g. Fx) is the relative frequency of its occurrence or the limit value of its relative frequency in the long run. Notation p(-) resp. p(Fx) Def Subjective probability /Schurz: the probability of a certain event or fact (e.g. Fa) is the rational degree of belief in the occurrence of an event by a given subject or all subjects of a rationality type, Notation: w(-) or w(Fa). >Probability/Schurz. I 111 Subjective probability: Pointe: Example coin toss: deviates from the objective probability! If more often number comes, one must assume that the coin is asymmetrical! This assumption is not expressible in the objective probability at all. I 115 Probability theory/Schurz: problems: (b) subjective probability: justification problems. On what grounds should rational degrees of belief satisfy Kolmogorov axioms? What role should degrees of belief play in the goal of finding real truths? Solution/Ramsey/de Finetti: Bet. Bet/Betting Quotient/Ramsey/Schurz: thesis fair betting quotients of a person satisfy Kolmogorov Axioms A1 - A3 exactly if they are coherent, i.e. that there is no system where total loss is possible. VsRamsey/Schurz: A bet is not yet a rational behavior in the sense of a search for truth! They are not truth-seeking, because the definition of the fair betting ratio refers only to the subjective degrees of belief, not to objective probability. The real frequency of success is not touched at all. Ex Suppose a subjectivist enthusiastically accepts a bet, of 1 : 1, that he will roll a six. He is fair if he is also willing to accept the opposite bet, 1 : 1 that he will not roll a six. Problem: he remains coherent and fair even if he has lost his entire fortune. He will only be surprised that no one will accept the counter bets he assumes to be fair. He cannot explain it as long as he is not allowed to consider the objective frequencies. This shows that the axioms A1 - A3 are at best a minimal condition. But this is too weak to exclude irrational behavior. I 115 Principal Principle/PP/Statistics/Schurz: the subjective probabilities, if the objective probabilities are known, must be consistent with them. Lewis: (1980)(1): singular PP: subjectivist. Here "objective" singular propensities are simply postulated. >Propensities. SchurzVsPropensity/SchurzVsPopper: it remains unclear what property a singular propensity should correspond to in the first place. Solution/de Finetti: one can also accept the objective notion of probability at the same time. Conditionalization/Statistics/Schurz: on an arbitrary experience datum E(b1...bn) over other individuals b1,..bn is important to derive two further versions of PP: 1. PP for random samples, which is needed for the subjective justification of the statistical likelihood intuition. 2. the conditional PP, for the principle of the closest reference class and subject to the inductive statistical specialization inference. >Probability theory. 1. Lewis, D. (1980). "A Subjectivist's Guide to Objective Chance". In: Jeffrey, R.C. (ed.)(1980), Studies in Inductive Logic and Probability, Vol 2, Berkeley: University of California Press. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Terminology | Lewis | Bigelow I 180 Definition Lagadonian Language/Lagadonian/Terminology/Swift/Lewis/Bigelow/Pargetter: by this name Lewis calls such a language, following Gulliver's travels. (1986a(1), p. 145). It is a set theoretical structure on individuals, characteristics, and relations. 1. Lewis, David 1986a. Philosophical Papers, Volume II, Oxford: Oxford University Press Schwarz I 97 Properties/Lewis/Schwarz: Definition intrinsic property: never differ between perfect duplicates. Duplicate: Defined not by sum, but by distribution of the perfectly natural property. Def Perfectly natural property: (PNP) = fundamental property: all qualitative intrinsic differences between things (also possible worlds) are based on their instantiation. - E.g. Fred is the tallest in his family, but his duplicate is not in his family. - that depends on distribution of intrinsic properties: if we duplicate the entire family, the duplicate is sure to be the tallest there as well. IV 58 Relation/individuation/Lewis: Relations are usually individuated through coextension. I-Relation/R-Relation/Lewis: These two relations are identical because they are coextensive. Def R-Relation/Identity/Continuity/Person/Lewis: a certain relation and connection among person states. Question: What conditions will survive the state in which you ask yourself this question? For example, if you walk out of a duplicator, who will you be, who will come out of the right or left door, or both? Def I-Relation/Lewis: Question: Which of the permanent persons are identical to the former? But of course there are also I-relations between the individual states! IV 259 Ramsey-sentence/Lewis: wipes out the difference between intensional and extensional language - at the same time it eliminates technical vocabulary by existential quantification. "Ramsification" neutral level: there is a system of categories, S, N, X/Y, there are three relationships of expressions to things: A-tension, B-tension, C-tension. I (b) 27 Theoretical Terms/TT/Lewis: (T terms) are names, not predicates or functions. I (b) 31 They can always be eliminabted by being replaced by their definientia. I (b) 34 Here: the T terms are names of mental states, the A terms are names for stimuli and responses and also for causal relationships. Theoretical terms: (T terms) are names, not predicates or functions. V 11 Compatibility/Possible world/Lewis: B is compatible with A in world i if an A world is closer to i than any non-B-world. - (Reversal of rather true) - then A were>>would C is true if C follows from A together with auxiliary hypotheses B1...Bn. - E.g. natural laws are compatible or completely incompatible with every assumption - thesis: then laws of nature are generalizations of what we consider to be particularly important. - Then conformity with Laws of Nature should be important for the similarity relation between possible worlds V 86 Principal Principle/main principle/probability/opportunity/Lewis: the Principal Principle is to be modeled according to our experience with direct conclusions. Exceptions: 1) it is about opportunity, not frequency. 2) Certainty of probabilities (opportunities) contributes to the resilience (resistance to new information). Schwarz I 99 Relations/Lewis: intrinsic: e.g., greater-relation (concerns only the two sides). Extrinsic: e.g. grandmother-relation (needs a third). Internal relation: (not equal to intrinsic relation): depends only on intrinsic properties and is reducible to them. External relation: is also intrinsic, but just not reducible. E.g., Spatiotemporal relation: "intrinsic with respect to pairs". Identity/partial relation/elementarity/Lewis: These are all no relations! |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 Schw I W. Schwarz David Lewis Bielefeld 2005 |
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| Disputed term/author/ism | Author Vs Author |
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Reference |
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| Antireductionism | Lewis Vs Antireductionism | Schwarz I 216 Possible Worlds/poss.w./meaning/conditional theory/Lewis/Schwarz: e.g. objects can only be a possible world if there is a corresponding object for each mode a world could be. This is why possible worlds cannot be sets of common sentences since there is not enough of them. ((s) >Language has not enough sentences to express all the possibilities.) >Ersatz Worlds as sets of sentences. Possible World/LewisVsAnti-Reductionism/Schwarz: interestingly, he is also using the same argument against anti-reductionist theories for which possible worlds are basic metaphysical facts. The name "possible world in which donkeys are able to talk" can only be given to an object if it somehow represents talking donkeys. Schwarz I 217 Possible World/representation/Lewis/Schwarz: for Lewis, possible worlds are nothing else than 1:1 models. How can this work for irreducible abstract entities? This is why it remains open whether proposed candidates actually could be possible worlds (1986e, 184)(1). Problem: some basic entities do not fulfill those conditions (if reduction failed). Not even in Laws of Nature (LoN) and objective probabilities. Objective probability is characterized by the Principal Principle and therefore implies subjective probability. But why should I assume that an event is going to happen only because I learn that an irreducible element, which is logically independent from the event happening, possesses the value 0.9 (1994a,239)(2)?. This is why something should not be called "chance". Reference/Lewis: reference therefore represents a sort of theory of definite description of the reference. Thesis: terms such as "possible world", "meaning", "pain", "objective probability" are associated with roles which describe what they refer to. How those roles are defined is explained by Lewis in "How to define theoretical terms" (1970c)(3). >Theoretical Terms. 1. D. Lewis [1986e]: On the Plurality of Worlds. Malden (Mass.): Blackwell. 2. D. Lewis [1994a]: “Humean Supervenience Debugged”. Mind, 103: 473–490. 3. D. Lewis [1970c]: “How to Define Theoretical Terms”. Journal of Philosophy, 67: 427–446. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Popper, K. | Schurz Vs Popper, K. | I 115 Principal Principle/PP/Statistics/Schurz: the subjective probabilities must agree with them when the objective probabilities are known. Lewis: (1980): singular principal principle: subjectivist. Here "objective" singular propensities are simply postulated. SchurzVsPropensity/SchurzVsPopper: it remains unclear which property a singular propensity should correspond to at all. Solution/de Finetti: you can also accept the objective probability concept at the same time. Conditionalization/Statistics/Schurz: on any experience date E(b1...bn) about other individuals b1,...bn it is important to derive two further versions of the principal principle: 1. Principal Principle for random samples used for the subjective justification of statistical likelihood intuition 2. The conditional principal principle, for the principle of narrowest reference class and the inductive statistical specialization conclusion is subject. Principal Principle: w(Fa I p(Fx) = r u E(b1,...bn)) = r Principal Principle for random samples: w(hn(Fx) = k/n I p(Fx) = r) = (nk) rk mal (1 r)n-k. Conditional Principal Principle: w(Fa I Ga u p(Fx I Gx) = r u E(b1,…bn)) = r. Principal Principle: is only useful for subjective a priori probabilities. I.e. belief degrees of a subject who has not yet had any experience. Actual Belief Degree/Belief Degree: the principle does not apply generally for it: for example if the coin is already showing head (=Fa) the belief degree of it is of course = 1, while one knows that p(Fx) = ½. Apriori probability function: here all background knowledge W must be explicitly written into the antecedens of a conditional probability statement w( - I W). actual: = personalistic. apriori probability: connection with updated probability function: Strict Conditionalization/Schurz: w0 is the a priori probability or probability to t0 and w1 the current probability. I 116 Wt is the knowledge acquired between t0 and t1. Then for any A applies: Wt(A) = w0(A I Wt). Narrowest reference class/n.r.c./Principle/Schurz: can be justified as follows: for a given event Fa, the individual can belong to a great many reference classes that assign very different probabilities to Fx. Then we got contradictory predictions. Question: but why should the appropriate reference class be the narrowest? Because one can prove that it maximizes the frequency value of true predictions. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
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